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AMRLS.cpp
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AMRLS.cpp
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// ----------------------------------------------------------------------------
//
// Copyright (c) 2019 - 2021 by the OpFlow developers
//
// This file is part of OpFlow.
//
// OpFlow is free software and is distributed under the MPL v2.0 license.
// The full text of the license can be found in the file LICENSE at the top
// level directory of OpFlow.
//
// ----------------------------------------------------------------------------
#include <OpFlow>
#include <fmt/chrono.h>
#include <fmt/compile.h>
using namespace OpFlow;
template <std::size_t d>
using DU = D1WENO53Upwind<d>;
template <std::size_t d>
using DD = D1WENO53Downwind<d>;
void amrls() {
using Mesh = CartesianAMRMesh<Meta::int_<2>>;
using Field = CartAMRField<Real, Mesh>;
constexpr int n = 65, maxlevel = 3, ratio = 2, buffWidth = 5;
constexpr auto h = 1. / (n - 1);
auto m = MeshBuilder<Mesh>()
.setBaseMesh(MeshBuilder<CartesianMesh<Meta::int_<2>>>()
.newMesh(n, n)
.setMeshOfDim(0, 0., 1.)
.setMeshOfDim(1, 0., 1.)
.build())
.setRefinementRatio(ratio)
.setFillRateThreshold(0.8)
.setSlimThreshold(buffWidth)
.setBuffWidth(buffWidth)
.setMaxLevel(maxlevel)
.setMarkerFunction([&](auto&& i) {
auto l = i.l;
double cx = 0.5, cy = 0.75;
double radius = 0.15;
double ht = h / Math::int_pow(ratio, l);
double eps = buffWidth * h / Math::int_pow(ratio, maxlevel - 1);
double x[4], y[4];
x[0] = x[2] = ht * i[0];
x[1] = x[3] = ht * (i[0] + 1);
y[0] = y[1] = ht * i[1];
y[2] = y[3] = ht * (i[1] + 1);
double r[4];
r[0] = (x[0] - cx) * (x[0] - cx) + (y[0] - cy) * (y[0] - cy);
r[1] = (x[1] - cx) * (x[1] - cx) + (y[1] - cy) * (y[1] - cy);
r[2] = (x[2] - cx) * (x[2] - cx) + (y[2] - cy) * (y[2] - cy);
r[3] = (x[3] - cx) * (x[3] - cx) + (y[3] - cy) * (y[3] - cy);
bool allin = true, allout = true;
auto r_min = std::max(0., radius - eps);
for (double k : r) {
allin &= (k < r_min * r_min);
allout &= (k > (radius + eps) * (radius + eps));
}
if (!allin && !allout) return true;
else
return false;
})
.build();
auto u = ExprBuilder<Field>()
.setMesh(m)
.setName("u")
.setLoc({LocOnMesh::Center, LocOnMesh ::Center})
.setBC(0, DimPos::start, BCType::Dirc, 0.)
.setBC(0, DimPos::end, BCType::Dirc, 0.)
.setBC(1, DimPos::start, BCType::Dirc, 0.)
.setBC(1, DimPos::end, BCType::Dirc, 0.)
.build();
auto v = u;
v.name = "v";
auto p = ExprBuilder<Field>()
.setName("p")
.setMesh(m)
.setBC(0, DimPos::start, BCType::Neum, 0.)
.setBC(0, DimPos::end, BCType::Neum, 0.)
.setBC(1, DimPos::start, BCType::Neum, 0.)
.setBC(1, DimPos::end, BCType::Neum, 0.)
.setLoc({LocOnMesh::Center, LocOnMesh::Center})
.build();
p.initBy([](auto&& x) { return std::sqrt(Math::pow2(x[0] - 0.5) + Math::pow2(x[1] - 0.75)) - 0.15; });
auto p1 = p, p2 = p, p3 = p, p0 = p;
u.initBy([](auto&& x) {
return 2 * std::sin(PI * x[1]) * std::cos(PI * x[1]) * Math::pow2(std::sin(PI * x[0]));
});
v.initBy([](auto&& x) {
return -2 * std::sin(PI * x[0]) * std::cos(PI * x[0]) * Math::pow2(std::sin(PI * x[1]));
});
auto _fmt = FMT_COMPILE("Result_{:%m-%d_%H-%M-%S}/");
auto root = fmt::format(_fmt, fmt::localtime(std::time(nullptr)));
Utils::VTKAMRStream uf(root + "u"), vf(root + "v"), pf(root + "p"), p1f(root + "p1"), p2f(root + "p2"),
p3f(root + "p3");
uf << Utils::TimeStamp(0) << u;
vf << Utils::TimeStamp(0) << v;
pf << Utils::TimeStamp(0) << p;
auto dt = 1. / ((n - 1) * Math::int_pow(ratio, maxlevel - 1));
auto refine_cond = (p > buffWidth * -h / Math::int_pow(ratio, maxlevel - 1))
&& (p < buffWidth * h / Math::int_pow(ratio, maxlevel - 1));
auto _eps = 1e-6;
auto _1 = [&](auto&& _p, auto&& _pp) {
return _p / OpFlow::sqrt(_p * _p + _eps)
* (OpFlow::sqrt(
OpFlow::pow(
OpFlow::max(-OpFlow::min(0., dx<DU>(_pp)), OpFlow::max(dx<DD>(_pp), 0.)), 2)
+ OpFlow::pow(
OpFlow::max(-OpFlow::min(0., dy<DU>(_pp)), OpFlow::max(dy<DD>(_pp), 0.)),
2))
- 1.);
};
auto _2 = [&](auto&& _p, auto&& _pp) {
return _p / OpFlow::sqrt(_p * _p + _eps)
* (OpFlow::sqrt(
OpFlow::pow(
OpFlow::max(OpFlow::max(0., dx<DU>(_pp)), -OpFlow::min(dx<DD>(_pp), 0.)), 2)
+ OpFlow::pow(
OpFlow::max(OpFlow::max(0., dy<DU>(_pp)), -OpFlow::min(dy<DD>(_pp), 0.)),
2))
- 1.);
};
for (auto i = 1; i < 4. / dt; ++i) {
p1 = p
- dt
* (u * conditional(u > 0., dx<DD>(p), dx<DU>(p))
+ v * conditional(v > 0., dy<DD>(p), dy<DU>(p)));
p2 = (p1
- dt
* (u * conditional(u > 0., dx<DD>(p1), dx<DU>(p1))
+ v * conditional(v > 0., dy<DD>(p1), dy<DU>(p1))))
/ 4.
+ 0.75 * p;
p3 = (p2
- dt
* (u * conditional(u > 0., dx<DD>(p2), dx<DU>(p2))
+ v * conditional(v > 0., dy<DD>(p2), dy<DU>(p2))))
* 2. / 3.
+ p / 3.;
p = p3;
p0 = p;
// reinit
for (auto _ = 0; _ < 4; ++_) {
constexpr auto h_min = h / Math::int_pow(ratio, maxlevel - 1);
auto h1 = conditional(p0 > 0, _1(p0, p), _2(p0, p));
p1 = p - dt * h1;
auto h2 = conditional(p0 > 0, _1(p0, p1), _2(p0, p1));
p2 = p1 - dt / 4. * (-3 * h1 + h2);
auto h3 = conditional(p0 > 0, _1(p0, p2), _2(p0, p2));
p3 = p2 - dt / 12. * (-h1 - h2 + 8 * h3);
constexpr auto _c = 16. / 24., _o = 1. / 24.;
constexpr DS::FixedSizeTensor<double, 3, 3> conv_ker {_o, _o, _o, _o, _c, _o, _o, _o, _o};
constexpr auto func = [=](Real d) { return Math::smoothDelta(h_min, d); };
constexpr auto functor = Utils::NamedFunctor<func, Utils::makeCXprString("smoothDelta")>();
constexpr auto delta_op
= [=](auto&& e) { return makeExpression<UniOpAdaptor<functor>>(OP_PERFECT_FOWD(e)); };
constexpr auto int_op = [=](auto&& e) { return h * h * conv(OP_PERFECT_FOWD(e), conv_ker); };
auto lambda = -int_op(delta_op(p0) * (p3 - p0) / (_ + 1)) / int_op(pow(delta_op(p0), 2) + 1e-14);
p = p3 + lambda * (_ + 1) * delta_op(p0);
}
pf << Utils::TimeStamp(i) << p;
refine_cond.prepare();
auto m2 = MeshBuilder<Mesh>()
.setRefMesh(p.mesh)
.setRefinementRatio(ratio)
.setFillRateThreshold(0.8)
.setSlimThreshold(buffWidth)
.setMaxLevel(maxlevel)
.setBuffWidth(buffWidth)
.setMarkerFunction([&](auto&& k) { return refine_cond.evalAt(k); })
.build();
p.replaceMeshBy(m2);
p1.replaceMeshBy(m2);
p2.replaceMeshBy(m2);
p3.replaceMeshBy(m2);
p0.replaceMeshBy(m2);
u.replaceMeshBy(m2);
v.replaceMeshBy(m2);
OP_INFO("Current step: {}", i);
}
}
void amrls_3d() {
using Mesh = CartesianAMRMesh<Meta::int_<3>>;
using Field = CartAMRField<Real, Mesh>;
constexpr int n = 17, maxlevel = 4, ratio = 4, buffWidth = 5;
constexpr auto h = 1. / (n - 1);
auto m = MeshBuilder<Mesh>()
.setBaseMesh(MeshBuilder<CartesianMesh<Meta::int_<3>>>()
.newMesh(n, n, n)
.setMeshOfDim(0, 0., 1.)
.setMeshOfDim(1, 0., 1.)
.setMeshOfDim(2, 0., 1.)
.build())
.setRefinementRatio(ratio)
.setFillRateThreshold(0.8)
.setSlimThreshold(buffWidth)
.setBuffWidth(buffWidth)
.setMaxLevel(maxlevel)
.setMarkerFunction([&](auto&& i) {
auto l = i.l;
double cx = 0.35, cy = 0.35, cz = 0.35;
double radius = 0.15;
double ht = h / Math::int_pow(ratio, l);
double eps = buffWidth * h / Math::int_pow(ratio, maxlevel - 1);
double x[8], y[8], z[8];
x[0] = x[2] = x[4] = x[6] = ht * i[0];
x[1] = x[3] = x[5] = x[7] = ht * (i[0] + 1);
y[0] = y[1] = y[5] = y[4] = ht * i[1];
y[2] = y[3] = y[6] = y[7] = ht * (i[1] + 1);
z[0] = z[1] = z[2] = z[3] = ht * i[2];
z[4] = z[5] = z[6] = z[7] = ht * (i[2] + 1);
double r[8];
r[0] = (x[0] - cx) * (x[0] - cx) + (y[0] - cy) * (y[0] - cy)
+ (z[0] - cz) * (z[0] - cz);
r[1] = (x[1] - cx) * (x[1] - cx) + (y[1] - cy) * (y[1] - cy)
+ (z[1] - cz) * (z[1] - cz);
r[2] = (x[2] - cx) * (x[2] - cx) + (y[2] - cy) * (y[2] - cy)
+ (z[2] - cz) * (z[2] - cz);
r[3] = (x[3] - cx) * (x[3] - cx) + (y[3] - cy) * (y[3] - cy)
+ (z[3] - cz) * (z[3] - cz);
r[4] = (x[4] - cx) * (x[4] - cx) + (y[4] - cy) * (y[4] - cy)
+ (z[4] - cz) * (z[4] - cz);
r[5] = (x[5] - cx) * (x[5] - cx) + (y[5] - cy) * (y[5] - cy)
+ (z[5] - cz) * (z[5] - cz);
r[6] = (x[6] - cx) * (x[6] - cx) + (y[6] - cy) * (y[6] - cy)
+ (z[6] - cz) * (z[6] - cz);
r[7] = (x[7] - cx) * (x[7] - cx) + (y[7] - cy) * (y[7] - cy)
+ (z[7] - cz) * (z[7] - cz);
bool allin = true, allout = true;
auto r_min = std::max(0., radius - eps);
for (double k : r) {
allin &= (k < r_min * r_min);
allout &= (k > (radius + eps) * (radius + eps));
}
if (!allin && !allout) return true;
else
return false;
})
.build();
auto u = ExprBuilder<Field>()
.setMesh(m)
.setName("u")
.setLoc({LocOnMesh::Center, LocOnMesh ::Center, LocOnMesh ::Center})
.setBC(0, DimPos::start, BCType::Dirc, 0.)
.setBC(0, DimPos::end, BCType::Dirc, 0.)
.setBC(1, DimPos::start, BCType::Dirc, 0.)
.setBC(1, DimPos::end, BCType::Dirc, 0.)
.setBC(2, DimPos::start, BCType::Dirc, 0.)
.setBC(2, DimPos::end, BCType::Dirc, 0.)
.build();
auto v = u;
v.name = "v";
auto w = u;
w.name = "w";
auto p = ExprBuilder<Field>()
.setName("p")
.setMesh(m)
.setBC(0, DimPos::start, BCType::Neum, 0.)
.setBC(0, DimPos::end, BCType::Neum, 0.)
.setBC(1, DimPos::start, BCType::Neum, 0.)
.setBC(1, DimPos::end, BCType::Neum, 0.)
.setBC(2, DimPos::start, BCType::Neum, 0.)
.setBC(2, DimPos::end, BCType::Neum, 0.)
.setLoc({LocOnMesh::Center, LocOnMesh::Center, LocOnMesh ::Center})
.build();
p.initBy([](auto&& x) {
return std::sqrt(Math::pow2(x[0] - 0.35) + Math::pow2(x[1] - 0.35) + Math::pow2(x[2] - 0.35)) - 0.15;
});
auto p1 = p, p2 = p, p3 = p, p0 = p;
u.initBy([](auto&& x) {
return 2 * Math::pow2(std::sin(PI * x[0])) * std::sin(2 * PI * x[1]) * std::sin(2 * PI * x[2]);
});
v.initBy([](auto&& x) {
return -std::sin(2 * PI * x[0]) * Math::pow2(std::sin(PI * x[1])) * std::sin(2 * PI * x[2]);
});
w.initBy([](auto&& x) {
return -std::sin(2 * PI * x[0]) * std::sin(2 * PI * x[1]) * Math::pow2(std::sin(PI * x[2]));
});
auto _fmt = FMT_COMPILE("Result_{:%m-%d_%H-%M-%S}/");
auto root = fmt::format(_fmt, fmt::localtime(std::time(nullptr)));
Utils::VTKAMRStream uf(root + "u"), vf(root + "v"), wf(root + "w"), pf(root + "p"), p1f(root + "p1"),
p2f(root + "p2"), p3f(root + "p3");
uf << Utils::TimeStamp(0) << u;
vf << Utils::TimeStamp(0) << v;
wf << Utils::TimeStamp(0) << w;
pf << Utils::TimeStamp(0) << p;
auto dt = 1. / 3. / ((n - 1) * Math::int_pow(ratio, maxlevel - 1));
auto refine_cond = (p > buffWidth * -h / Math::int_pow(ratio, maxlevel - 1))
&& (p < buffWidth * h / Math::int_pow(ratio, maxlevel - 1));
auto _eps = 1e-6;
auto _1 = [&](auto&& _p, auto&& _pp) {
return _p / OpFlow::sqrt(_p * _p + _eps)
* (OpFlow::sqrt(
OpFlow::pow(
OpFlow::max(-OpFlow::min(0., dx<DU>(_pp)), OpFlow::max(dx<DD>(_pp), 0.)), 2)
+ OpFlow::pow(
OpFlow::max(-OpFlow::min(0., dy<DU>(_pp)), OpFlow::max(dy<DD>(_pp), 0.)), 2)
+ OpFlow::pow(
OpFlow::max(-OpFlow::min(0., dz<DU>(_pp)), OpFlow::max(dz<DD>(_pp), 0.)),
2))
- 1.);
};
auto _2 = [&](auto&& _p, auto&& _pp) {
return _p / OpFlow::sqrt(_p * _p + _eps)
* (OpFlow::sqrt(
OpFlow::pow(
OpFlow::max(OpFlow::max(0., dx<DU>(_pp)), -OpFlow::min(dx<DD>(_pp), 0.)), 2)
+ OpFlow::pow(
OpFlow::max(OpFlow::max(0., dy<DU>(_pp)), -OpFlow::min(dy<DD>(_pp), 0.)), 2)
+ OpFlow::pow(
OpFlow::max(OpFlow::max(0., dz<DU>(_pp)), -OpFlow::min(dz<DD>(_pp), 0.)),
2))
- 1.);
};
for (auto i = 1; i < 4. / dt; ++i) {
p1 = p
- dt
* (u * conditional(u > 0., dx<DD>(p), dx<DU>(p))
+ v * conditional(v > 0., dy<DD>(p), dy<DU>(p))
+ w * conditional(w > 0., dz<DD>(p), dz<DU>(p)));
p2 = (p1
- dt
* (u * conditional(u > 0., dx<DD>(p1), dx<DU>(p1))
+ v * conditional(v > 0., dy<DD>(p1), dy<DU>(p1))
+ w * conditional(w > 0., dz<DD>(p1), dz<DU>(p1))))
/ 4.
+ 0.75 * p;
p3 = (p2
- dt
* (u * conditional(u > 0., dx<DD>(p2), dx<DU>(p2))
+ v * conditional(v > 0., dy<DD>(p2), dy<DU>(p2))
+ w * conditional(w > 0., dz<DD>(p2), dz<DU>(p2))))
* 2. / 3.
+ p / 3.;
p = p3;
p0 = p;
// reinit
for (auto _ = 0; _ < 2; ++_) {
constexpr auto h_min = h / Math::int_pow(ratio, maxlevel - 1);
auto h1 = conditional(p0 > 0, _1(p0, p), _2(p0, p));
p1 = p - dt * h1;
auto h2 = conditional(p0 > 0, _1(p0, p1), _2(p0, p1));
p2 = p1 - dt / 4. * (-3 * h1 + h2);
auto h3 = conditional(p0 > 0, _1(p0, p2), _2(p0, p2));
p3 = p2 - dt / 12. * (-h1 - h2 + 8 * h3);
constexpr auto _c = 64. / 90., _o = 1. / 90.;
constexpr DS::FixedSizeTensor<double, 3, 3, 3> conv_ker {_o, _o, _o, _o, _o, _o, _o, _o, _o,
_o, _o, _o, _o, _c, _o, _o, _o, _o,
_o, _o, _o, _o, _o, _o, _o, _o, _o};
constexpr auto func = [=](Real d) { return Math::smoothDelta(1.5 * h_min, d); };
constexpr auto functor = Utils::NamedFunctor<func, Utils::makeCXprString("smoothDelta")>();
constexpr auto delta_op
= [=](auto&& e) { return makeExpression<UniOpAdaptor<functor>>(OP_PERFECT_FOWD(e)); };
constexpr auto int_op = [=](auto&& e) { return h * h * conv(OP_PERFECT_FOWD(e), conv_ker); };
auto lambda = -int_op(delta_op(p0) * (p3 - p0) / (_ + 1)) / int_op(pow(delta_op(p0), 2) + 1e-14);
p = p3 + lambda * (_ + 1) * delta_op(p0);
}
if (i % 30 == 0) pf << Utils::TimeStamp(i) << p;
refine_cond.prepare();
auto m2 = MeshBuilder<Mesh>()
.setRefMesh(p.mesh)
.setRefinementRatio(ratio)
.setFillRateThreshold(0.8)
.setSlimThreshold(buffWidth)
.setMaxLevel(maxlevel)
.setBuffWidth(buffWidth)
.setMarkerFunction([&](auto&& k) { return refine_cond.evalAt(k); })
.build();
p.replaceMeshBy(m2);
p1.replaceMeshBy(m2);
p2.replaceMeshBy(m2);
p3.replaceMeshBy(m2);
p0.replaceMeshBy(m2);
u.replaceMeshBy(m2);
v.replaceMeshBy(m2);
w.replaceMeshBy(m2);
u.initBy([](auto&& x) {
return 2 * Math::pow2(std::sin(PI * x[0])) * std::sin(2 * PI * x[1]) * std::sin(2 * PI * x[2]);
});
v.initBy([](auto&& x) {
return -std::sin(2 * PI * x[0]) * Math::pow2(std::sin(PI * x[1])) * std::sin(2 * PI * x[2]);
});
w.initBy([](auto&& x) {
return -std::sin(2 * PI * x[0]) * std::sin(2 * PI * x[1]) * Math::pow2(std::sin(PI * x[2]));
});
OP_INFO("Current step: {}", i);
}
}